slantp (l) - Linux Manuals
slantp: returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
Command to display slantp
manual in Linux: $ man l slantp
NAME
SLANTP - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
SYNOPSIS
- REAL FUNCTION
-
SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
-
CHARACTER
DIAG, NORM, UPLO
-
INTEGER
N
-
REAL
AP( * ), WORK( * )
PURPOSE
SLANTP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
triangular matrix A, supplied in packed form.
DESCRIPTION
SLANTP returns the value
SLANTP
= ( max(abs(A(i,j))), NORM = aqMaq or aqmaq
(
( norm1(A), NORM = aq1aq, aqOaq or aqoaq
(
( normI(A), NORM = aqIaq or aqiaq
(
( normF(A), NORM = aqFaq, aqfaq, aqEaq or aqeaq
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
ARGUMENTS
- NORM (input) CHARACTER*1
-
Specifies the value to be returned in SLANTP as described
above.
- UPLO (input) CHARACTER*1
-
Specifies whether the matrix A is upper or lower triangular.
= aqUaq: Upper triangular
= aqLaq: Lower triangular
- DIAG (input) CHARACTER*1
-
Specifies whether or not the matrix A is unit triangular.
= aqNaq: Non-unit triangular
= aqUaq: Unit triangular
- N (input) INTEGER
-
The order of the matrix A. N >= 0. When N = 0, SLANTP is
set to zero.
- AP (input) REAL array, dimension (N*(N+1)/2)
-
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = aqLaq, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
Note that when DIAG = aqUaq, the elements of the array AP
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.
- WORK (workspace) REAL array, dimension (MAX(1,LWORK)),
-
where LWORK >= N when NORM = aqIaq; otherwise, WORK is not
referenced.
Pages related to slantp
- slantp (3)
- slantb (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
- slantr (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
- slaneg (l) - computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - sigma I = L D L^T
- slangb (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
- slange (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
- slangt (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
- slanhs (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
- slansb (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
- slansf (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A in RFP format